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Right now, you can get a fairly complete basic setup of decent-quality camping gear from Moosejaw's online shop.
I recommend a Kelty freestanding (freestanding means it doesn't need to be staked) 2-person (not too constricted, room for gear) tent. The Discovery Trail 2P costs $90 off Moosejaw right now and weighs a bit over 4 lbs.
To get down to a 2 lb.ish tent made of tanned unicorn twats, you need to start shitting out hundreds of dollars. Don't.
A Kelty sleeping bag and basic foldable foam sleeping pad will be good. I used a rolled-up foam pad for years, and rolling it tight was always a bitch.
Get some type of water purification device (NOT LifeStraw, they are for emergencies and suck to use) like a Katadyn pump filter. Google up basic info on water purification. Any water bottle you already have will do. I love the Platypus soft plastic bottles, as they fold up to nothing when empty and are rugged (for soft plastic, anyway). Avoid integrated bladder systems, they're annoying as fuck.
Like other anons said, headlamp. Buy two or even three. You don't need the $50+ ones. I use a HeroBeam for both catfishing and camping, but a handful of cheapos from Walmart in a Ziploc would be good.
If you want general illumination, get an LED lantern or a cheap-ish LED kayak light. Reason is kayak lights can be hung in your tent, but unlike meme lights they'll also work for night boating if you ever go that way.
No other anon had mentioned this yet because they're all LARPers and consider themselves to be Paul Bunyan/Rambo hybrids, but tell a friend or relative your itinerary. I'd nothing else, it'll help the rangers recover your remains.
Learn navigation before even going out of sight of a road, even in a park full of faggot Instagrammers and lardass trailer trash. Learn to use a compass and an old-fashioned map. It's a skill worth having. Until then, rely on your gay-ass iPhone with some OFFLINE maps. Consider a waterproof, floating phone case.
Bring entertainment.
